Asymptotic formulae for implied volatility in the Heston model

By Martin Forde, Antoine Jacquier, Aleksandar Mijatovic. Proceedings of the Royal Society A, 2009

59 citations recorded by the source corpus.

In this paper, we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first-order terms in the large maturity expansion of the implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2dd32bb82bed3ea2e4ddac94e5b49d8739f19071

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Antoine Jacquier
2. Jim Gatheral
3. Eduardo Abi Jaber
4. Mathieu Rosenbaum
5. Masaaki Fukasawa
6. Omar El Euch
7. Peter K. Friz
8. Christoph Frei

In Mathematical Physics

1. Jim Gatheral
2. Antoine Jacquier

Citations in the corpus

• Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, unknown): “Additional information is given in [51], [62].”
• Convergence of Heston to SVI (2010, background): “In this short note, we prove by an appropriate change of variables that the SVI implied volatility parameterization presented in [2] and the large-time asymptotic of the Heston implied volatility derived in [1] agree algebraically, thus confirming a conjecture from [2] as well as providing a simpler”